In order for a temporal ordinal reference system (TM_OrdinalReferenceSystem, abbrev. TORS) to unambiguously define the relative temporal position of named TM_OrdinalEras that are aggretated to form the system, the TORS must be linked to a particular kind of temporal topological complex. The constraint is that only one path between any two nodes in the complex may be subdivided. The accompanying schema models this as ‘UnambiguousTemporalTopoComplex’, a subtype of TM_TopologicalComplex.

This temporal topologic complex actually the essence of a geologic time system. Historically, the time scale evolved as an ordinal reference system, which is inherently topological. The ability to locate the nodes in this topology using a TM_CoordinateSystem based on various isotopic decay systems is a recent overlay.

Each TM_OrdinalEra names a particular TM_edge in the temporal topological complex associated with the TORS. Because the eras may have parts (members), they must have some duration (they name edges, not nodes, and have corresponding TM_periods).

GeologicTimeSystem is a kind of TM_ReferenceSystem, in which the eras are names for edges in an associated unambiguous temporal topologic complex.

ISO 19108 defines a TORS as composed of TM_OrdinalEras, not TM_Edges. In the accompanying model, the ‘StratEra’ subtype of TM_OrdinalEra has "begin" and "end" properties that point to StratNodes, a subtype of TM_Node. (These are equivalent to the ‘begin’ and ‘end’ links from the TM_edge named by the StratEra) The "begin" and "end" attributes on ISO 19108 TM_OrdinalEra, which have 0..1 cardinality and datatype DateTime, are null (cardinality ‘0’) for StratEra instances.

-- SimonCox - 30 Jun 2004

I'm assuming TimeNode? is equivalent to TM_node from the TM_TopologicalComplex model (19108, p. 14). I think I'm finally starting to see the problem. Essentially, a TM_OrdinalEra is a named edge from a TM_TopoComplex. Thus it is subtyped from Definition; it's a term for a conceptual thing. The TORS is a collection of terms that correspond to a special kind of TM_TopoComplex (only one of any pair of parallel branches may be subdivided.) As it is currently modeled, the ordering of events in a TOR is not explicitly modeled, but implicit in the begin and end properties. These are DateTime? objects, which don't allow representation of uncertainty about the time position of the interval boundary._ Your solution implies a 1:1 association between TM_OrdinalEra and a TM_Edge defined by the 'start' and 'end' property role fillers (unless the cardinalities are 0..1?). Isn't there a constraint, necessary but not stated, that the TimeNode? and TimeOrdinalEras? must form a topo complex such that there are no 'gaps' in the TORS?

So a possible solution is to pull the 'begin' and 'end' attributes from TOR, link TOR with TM_Edge (1:1), so start and end for TOR come through the TM_Edge. The ordering of TM_OrdinalEras is modeled through the structure of the associated topo complex (which conforms to the TOR constraint on a topo complex).

Doesn't the 'RelativePosition' association from TimeOdinalEra? (XMML GeoTimeSystems? model) to TimePrimitive? essentially model the TOR in a general temporal topological complex, where edges may overlap? Hmmm...

-- SteveRichard - 30 Jun 2004

it looks to me like there are 3 fundamental kinds of TRS--periodic/astronomical (calendar and clock; counting periodic events), accumulative (accumulation of radioactive decay products, direct measure of duration based on some physical proxy), and relative (ordinal, based on causal ordering). Why not make these the top level TRS objects?

-- SteveRichard - 28 Jun 2004

Yes that could be done. But the geological time scale is a TORS (not just the post-Cryogenian piece) - it is intended that people can provide the age of an object using a word rather than a number, even for the pre-Ediacaran (though it is probably more common to use a number, i.e. a position on a time coordinate system, for the earlier piece). And the mechanical problem is that, as defined in 19108, a TORS is composed of TM_OrdinalEras, not TM_Edges. I tried to finesse the issue in GML - you will see that TimeOrdinalEra?, which is supposed to implement TM_OrdinalEra, replaces the "begin" and "end" attributes (which have DateTime? values) with "start" amd "end" properties (which point to TimeNodes?). The justification is

  1. the ISO UML are "conceptual" models while GML is an implementation (though this does not really justify adding complexity!)
  2. I've put in a change request to 19108 proposing this change: I discussed it with the 19108 editor and he confessed that, despite reference to geology as an archetypical TORS, they hadn't really factored in the fact that the positions of the boundaries are not known precisely, so the model is really broken in this place. I believe we have an opportunity to make the case now for why current best-practice in geoscience requires an amendment to the 19108 model along the lines we are discussing.

So my strategy in writing a paper now is twofold:

  1. to alert the stratigraphy community to the fact that there is a theory of TORS's described in an ISO standard, and that they would do themselves a favour by formalising their own model, as far as possible bringing it into alignment with 19108
  2. expose the current flaws in 19108 and prepare a well structured amendment (amendments to ISO standards have more weight if there is independent documentary evidence).